Final answer:
The given system of equations has infinitely many solutions. The correct option is C. Infinitely many solutions
Step-by-step explanation:
The given system of equations is:
4x - 10y = -20 -----(1)
6x - 15y = -30 -----(2)
We can start by simplifying the equations:
Multiplying equation (1) by 3, we get:
12x - 30y = -60 -----(3)
Subtracting equation (3) from equation (2), we eliminate x:
(6x - 15y) - (12x - 30y) = -30 - (-60)
-6x + 15y = 30
Next, divide this equation by -3 to simplify it further:
2x - 5y = -10 -----(4)
Now, we have two simplified equations:
2x - 5y = -10 -----(4)
4x - 10y = -20 -----(1)
By comparing the two equations, we can see that equation (4) is a multiple of equation (1).
This means that the two equations represent the same line and have infinitely many solutions.
The correct option is C. Infinitely many solutions